$\text { Use the Quotient Rule to differentiate the function } f ( x ) = \frac { \sin x } { x ^ { 2 } + 3 } \text {. }$

Multiple Choice

$\text { Use the Quotient Rule to differentiate the function } f ( x ) = \frac { \sin x } { x ^ { 2 } + 3 } \text {. }$

A)
$$f ^ {t } ( x ) = \frac { \left( 3 + x ^ { 2 } \right) \cos x + 2 x \sin x } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$$
B)
$$f ^ { t } ( x ) = \frac { \left( 3 + x ^ { 2 } \right) \cos x - 2 x \sin x } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$$
C)
$$f ^ { t } ( x ) = \frac { ( 3 + x ) \cos x - 2 x \sin x } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$$
D)
$$f ^ { t } ( x ) = \frac { \left( 3 - x ^ { 2 } \right) \cos x - 2 x \sin x } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$$
E)
$$f ^ { t} ( x ) = \frac { \left( 3 + x ^ { 2 } \right) \cos x - 2 x \sin x } { \left( x ^ { 2 } + 3 \right) }$$